Active sensor for micro force measurement

ABSTRACT

An active micro-force sensor is provided for use on a micromanipulation device. The active micro-force sensor includes a cantilever structure having an actuator layer of piezoelectric material and a sensing layer of piezoelectric material bonded together. When an external force is exerted on the sensor, the sensor deforms and an applied force signal is recorded by the sensing layer. The applied force signal is then fed back to the actuating layer of the sensor via a servoed transfer function or servo controller, so that a counteracting deformation can be generated by the bending moment from the servoed actuating layer to quickly balance the deformation caused by the external micro-force. Once balanced, the sensor beam comes back to straight status and the tip will remain in its equilibrium position, thus the sensor stiffness seems to be virtually improved so that the accurate motion control of the sensor tip can be reached, especially, at the same time, the micro-force can also be obtained by solving the counteracting balance voltage applied to the actuating layer.

FIELD OF THE INVENTION

The present invention relates generally to micromanipulation technologyand, more particularly, to an active micro-force sensor for use inmicromanipulation.

BACKGROUND OF THE INVENTION

Efficient assembly processes for micro devices have not been developed,partially because, at the micro-scale, structures are fragile and easilybreakable. Typically breakage at the micro-Newton force range cannot bereliably measured by most existing force sensors. So far the moststraightforward and flexible operation methods run in an open loopformat using a microprobe to physically manipulate the micro device.This method can be inherently risky without an on-line safety microforce regulation. As a result, this approach decreases overall yield anddrives up the cost of micro devices. For these reasons, research intoautomating the micromanipulation processes have focused on micro forcesensing and related control techniques.

In micro force sensing, cantilever beams are the most frequentlyimplemented sensor structure type depending on its highly sensitivefactor, and either static or dynamic operation mode. However,cantilever-based sensors introduce significant limitations formicro-force measurements during micromanipulation. First, thecantilever-based sensors have a relatively flexible structure whichcauses inherent difficulties with accurate manipulation of microdevices. Second, such sensors exhibit only a small dynamic range formaintaining high accuracy. To overcome these limitations, the presentinvention proposes an innovative active micro-force sensor based on thebilateral mechanical-electrical behaviors of piezoelectric films.

SUMMARY OF THE INVENTION

In accordance with the present invention, an improved active micro-forcesensor is provided for use on a micromanipulation device. The activemicro-force sensor includes a cantilever structure having an actuatorlayer of piezoelectric material and a sensing layer of piezoelectricmaterial symmetrically bonded together. When an external force isexerted on the sensor tip, the sensor beam deforms and an applied forcesignal is detected by the sensing layer. The applied force signal isthen fed back to the actuating layer of the sensor via a servoedtransfer function or servo controller so that a counteractingdeformation can be generated by the bend moment from the servoedactuating layer to quickly balance the deformation caused by theexternal micro-force. Once balanced, the sensor beam comes back tostraight status and the tip will remain in its equilibrium position,thus the sensor stiffness seems to be virtually improved so that theaccurate motion control of the sensor tip can be reached, especially, atthe same time, the micro-force can also be obtained by solving thecounteracting balance voltage applied to the actuating layer.

Further areas of applicability of the present invention will becomeapparent from the detailed description provided hereinafter. It shouldbe understood that the detailed description and specific examples, whileindicating the preferred embodiment of the invention, are intended forpurposes of illustration only and are not intended to limit the scope ofthe invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B are illustrations of two exemplary active micro-forcesensors in accordance with the present invention;

FIG. 2 is a schematic of an exemplary circuit for interfacing with themicro-force sensor of the present invention;

FIGS. 3A-3J are illustrations of the active micro-force sensor havingdifferent patterned electrode layers;

FIG. 4 is a block diagram of an active sensing and balance servo systemfor the micro-force sensor of the present invention;

FIGS. 5A and 5B are graphs illustrating the frequency response of theVa/Vs transfer function by simulation and experiment, respectively; and

FIG. 6 depicts an exemplary three-dimensional active micro-force sensorin accordance with the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIGS. 1A and 1B illustrates an active micro-force sensor for use on amicromanipulation device. The force sensor 10 is comprised of a rigidcontact tip 12 which extends outwardly from a cantilever 14. Thecantilever 14 is in turn coupled to an end of a micromanipulator 16. Itis readily understood that the contact tip 12 may have different shapesdepending on the applicable micromanipulation tasks.

In accordance with the present invention, the cantilever 14 is acomposite structure having at least two layers 22, 24 made from apiezoelectric material (e.g., polyvinylidene fluoride (PVDF) or leadzirconate titanate (PZT)). In operation, the top layer 22 acts as abalance actuator, while the bottom layer 24 works as a sensing device aswill be further explained below.

In FIG. 1A, the two layers 22, 24 are bonded directly together using aninsulating, waterproof, high strength, and elastic adhesive (e.g.Loctite® Super Glue Gel, Epoxy Gel or RTV Silicone) or other knownbonding technique (double side thin glue tape). In this exemplaryembodiment, the two piezoelectric layers are in the form of arectangular plate. However, it is readily understood that other types ofmaterials as well as other suitable shapes for the piezoelectric layersare within the scope of the present invention.

To provide an insulator between the layers 22, 24, it is envisioned thata thin support layer 26 may be interposed between the two outerpiezoelectric layers 22, 24 as shown in FIG. 1B. The support layer 26 ispreferably made from a polyester material with the function ofelectrostatic shielding, but other types of thin, elastic,electrostaticity-shielding, and insulating materials are also within thescope of the present invention. Again, the piezoelectric layers 22, 24are preferably bonded to each side of the support layer 26.

Principles behind an active micro-force sensor having a compositecantilever structure are further described below. Assuming the geometryof the cantilever is much wider and longer than its thickness, thestrain s_(y) along the width of the beam can be assumed to be zero.Based on piezoelectric transverse effect, the unit piezoelectricequation is (without considering the inverse piezoelectric affection andpyroelectric effects):D ₃(r,t)=d ₃₁σ_(s)(r,t)   (1)where D₃(r,t) is the normal electric displacement of a PVDF film, d₃₁ isthe transverse piezoelectric coefficient and σ_(s)(r,t) denotes the unitstress of the surface of the PVDF sensing layer along beam length.

The surface area polarization gives a charge Q_(s)(t) across the PVDFsensing layer active surface area A (covered by electrode):$\begin{matrix}\begin{matrix}{{Q_{s}(t)} = {\int{{D_{3}\left( {r,t} \right)}{\mathbb{d}A}}}} \\{= {\int{\int_{A}^{\quad}{{D_{3}\left( {r,t} \right)}\quad{\mathbb{d}y}{{\mathbb{d}r}.}}}}}\end{matrix} & (2)\end{matrix}$

Using the mechanics of materials for cantilever beam, as shown in FIG.1B, the unit stress on the surface of the PVDF sensing layer 24 can beobtained if the external load f_(c)(t) acts at the sensor tip$\begin{matrix}\begin{matrix}{{\sigma_{s}\left( {r,t} \right)} = {{- {cE}_{s}}\frac{\partial^{2}{\omega_{s}\left( {r,t} \right)}}{\partial r^{2}}}} \\{\doteq {\frac{{f_{c}(t)}\left( {L - r} \right)c}{I} + \frac{{f_{c}(t)}L_{0}c}{I}}}\end{matrix} & (3)\end{matrix}$Notice that since a three-layer composite beam is employed (omitting theeffect of thin electrode layers at the top and bottom surfaces of PVDFlayers), I will be the moment of the transformed cross section of thecomposite beam. The neutral axis c_(n) of the composite beam passesthrough the centroid of the transformed cross section. c is the distancebetween the middle of the PDF sensing layer and the neutral axis c_(n)of the composite beam. ω_(s)(r,t) is the elastic deflection of theflexible active composite beam caused by the micro force f_(c)(t) at thesensor tip, and 0≦r≦L. Here, the neutral axis of the composite beam canbe obtained by $\begin{matrix}{c_{n} = {\frac{{{WH}_{s}c_{s}} + {\frac{E_{m}}{E_{s}}{WH}_{m}c_{m}} + {{WH}_{a}c_{a}}}{A_{T}}.}} & (4)\end{matrix}$where E_(s)=E_(a), E_(m) are Young moduli of the two PVDF layers 22, 24and the polyester film, respectively. c_(s), c_(a), and c_(m) are thedistances of centroid axes of the two PVDF layers 22, 24, and thepolyester layer 26 with respect to the base axis of beam, respectively.H=H_(s)+H_(m)+H_(a) is the thickness of the whole composite beam. A_(T)is the total area of transformed cross section as follows:$\begin{matrix}{A_{T} = {{WH}_{s} + {\frac{E_{m}}{E_{s}}{WH}_{m}} + {{WH}_{a}.}}} & (5)\end{matrix}$Then, I, which is around the neutral axis, can be determined by$\begin{matrix}{I = {\frac{{WH}_{s}^{3}}{12} + {\frac{E_{m}}{E_{s}}\frac{{WH}_{m}^{3}}{12}} + \frac{{WH}_{a}^{3}}{12} + {{WH}_{s}\left( {\frac{H_{m}}{2} + \frac{H_{s}}{2}} \right)}^{2} + {{WH}_{a}\left( {\frac{H_{m}}{2} + \frac{H_{a}}{2}} \right)}^{2}}} & (6)\end{matrix}$

Since generation of charge is the same along the width of PVDF(s_(y)=0), we can rewrite equation (2) as: $\begin{matrix}\begin{matrix}{{Q_{s}(t)} = {\int_{0}^{L}\quad{{\mathbb{d}_{31}{\sigma_{s}\left( {r,t} \right)}}W{\mathbb{d}r}}}} \\{= {{{- {cE}_{s}}d_{31}W\frac{\partial{\omega_{s}\left( {r,t} \right)}}{\partial r}}❘_{0}^{L}}} \\{= {\frac{d_{31}{A\left( {L_{0} + \frac{L}{2}} \right)}c}{I}{{f_{c}(t)}.}}}\end{matrix} & (7)\end{matrix}$

Continually, a simplified and effective equivalent circuit model of acapacitor C_(P) can be used to represent the model of the PVDF sensinglayer 24. The output voltage V_(s)(t) of the PVDF sensing layer 24caused by the micro force can be described by $\begin{matrix}{{V_{s}(t)} = {\frac{Q_{s}(t)}{C_{P}}.}} & (8)\end{matrix}$

By Laplace transformation, the electrical transfer function of thesensing layer is given as: $\begin{matrix}{{V_{s}(s)} = {\frac{Q_{s}(s)}{C_{P}}.}} & (9)\end{matrix}$

To find the dynamic relationship between the sensing output V_(s) andthe micro force f_(c) acting at the senor tip, we first describe adynamic model of the flexible PVDF active sensor illustrated in FIG. 1B.Here, the partial differential equation describing the elasticdeflection of the flexible composite PVDF sensor is a Bernoulli-Eulerequation with an additional term due to the external force and moment.The equation is given by: $\begin{matrix}\begin{matrix}{{{{EI}\frac{\partial^{4}{\omega_{s}\left( {r,t} \right)}}{\partial r^{4}}} + {\rho\quad A\frac{\partial^{2}{\omega_{s}\left( {r,t} \right)}}{\partial t^{2}}}} = {{{f_{c}(t)}{\delta\left( {r - L} \right)}} +}} \\{{f_{c}(t)}L_{0}\frac{\partial\left( {{\delta\left( {r - 0} \right)} - {\delta\left( {r - L} \right)}} \right)}{\partial r}}\end{matrix} & (10)\end{matrix}$where E, I, L and p represent the Young's modulus, inertia moment,length of beam, and linear mass density of the composite beam. Assumingthat EI=E_(a)I_(a)+E_(m)I_(m)+E_(s)I_(s) is the flexural rigidity of theactive beam and pA=ρ_(a)A_(a)+ρ_(m)A_(m)+ρ_(s)A_(s) is mass per unitlength of the active beam. f_(c)(t) is the external force acting at thefree end of beam, which can be detected by the PVDF sensing layer 24.δ(.) denotes the Dirac delta function.

The boundary conditions for the above equation are: $\begin{matrix}{{\omega_{s}\left( {0,t} \right)} = 0} & (11) \\{{{EI}\frac{\partial{\omega_{s}\left( {o,t} \right)}}{\partial r}} = 0} & (12) \\{{{EI}\frac{\partial{\omega_{s}^{2}\left( {L,t} \right)}}{\partial r^{2}}} = {{f_{c}(t)}L_{0}}} & (13) \\{{{EI}\frac{\partial{\omega_{s}^{3}\left( {L,t} \right)}}{\partial r^{3}}} = {f_{c}(t)}} & (14)\end{matrix}$

By using the modal analysis method, we assume that the deformation ofthe beam have infinite shape modes, then the deflection ω_(s)(r,t) canbe expressed as an infinite series in the following form:$\begin{matrix}{{\omega_{s}\left( {r,t} \right)} = {\sum\limits_{i = 1}^{\infty}{{\Phi_{i}(r)}{q_{si}(t)}}}} & (15)\end{matrix}$where Φ_(i)(r) are the eigenfunction satisfying the ordinarydifferential equation and q_(si)(t)are the modal displacements caused bythe micro force. Then the deflection mode shapes are assumed to be:Φ_(i)(r)=C ₁ sin(α_(i) r)+C ₂ cos(α_(i) r)+C ₃ sin h(α_(i) r)+C ₄ cosh(α_(i) r)   (16)Substituting the above equations (15) and (16) into the boundaryconditions (11)˜(14) and taking advantage of the orthogonalityconditions, $\begin{matrix}{{{\int_{0}^{L}{{\Phi_{i}(r)}{\Phi_{j}(r)}\quad{\mathbb{d}r}}} = \delta_{ij}}\left\{ \begin{matrix}{{i = j},{\delta_{ij} = 1}} \\{{i \neq j},{\delta_{ij} = 0}}\end{matrix} \right.} & (17)\end{matrix}$where δ_(ij) is the Kronecker delta function, the mode shapes of thiscantilever beam are found to be in the form:Φ_(i)(r)=C _(r)[ cos(α_(i) r)−cos h(α_(i) r)+k _(L)(sin(α_(i) r)−sinh(α_(i) r))]  (18)where C_(r)=C₂, C₂≠0 is a constant,$k_{L} = \frac{{\sin\left( {\alpha_{i}L} \right)} - {\sin\quad{h\left( {\alpha_{i}L} \right)}}}{{\cos\left( {\alpha_{i}L} \right)} + {\cos\quad{h\left( {\alpha_{i}L} \right)}}}$and α_(i) are the infinite set of eigenvalues yielded by1+cos(α_(i) L)cos h(α_(i) L)=0   (19)and also, the natural frequencies a; of the sensor beam correspond tothe α_(i) by $\begin{matrix}{\omega_{i} = {\alpha_{i}^{2}\sqrt{\frac{EI}{pA}}}} & (20)\end{matrix}$

In order to determine the dynamics of the system, we use Lagrange'sequation of motion by $\begin{matrix}{{{\frac{\mathbb{d}}{\mathbb{d}t}\frac{\partial\left( {E_{sk} - E_{sp}} \right)}{\partial{\overset{.}{q}}_{si}}} - \frac{\partial\left( {E_{sk} - E_{sp}} \right)}{\partial q_{si}}} = Q_{i.}} & (21)\end{matrix}$Here, E_(sk) is the kinetic energy, E_(sp) represents the potentialenergy and Q_(i) is the generalized nonconservative forces related tothe external micro force. They are $\begin{matrix}{E_{sk} = {\frac{1}{2}{\int_{0}^{L}{{{\overset{.}{\omega}}_{s}\left( {r,t} \right)}^{2}\rho\quad A\quad{\mathbb{d}r}}}}} & (22) \\{{E_{sp} = {\frac{1}{2}{\int_{0}^{L}{{EI}\quad{\omega_{s}^{''}\left( {r,t} \right)}^{2}\quad{\mathbb{d}r}}}}}{Q_{i} = {{{f_{c}(t)}{\Phi_{i}(L)}} + {{f_{c}(t)}{L_{0}\left\lbrack {{\Phi_{i}^{\prime}(L)} - {\Phi_{i}^{\prime}(0)}} \right\rbrack}}}}} & (23)\end{matrix}$where a prime indicates the derivative with respect to position and adot denotes the derivative with respect to time.

Using the Lagrange's equation of motion (21) and orthogonalityconditions (17) and (20), we have the differential equationcorresponding to each shape mode of the sensor beam to beEIα _(i) ⁴ q _(si)(t)+ρA{umlaut over (q)}_(si)(t)=f _(c)(t)Φ_(i)(L)+f_(c)(t)L ₀[Φ′_(i)(L)−Φ′_(i)(0)]  (24)Then by the Laplace transformation of the above equation, the dynamicrelationship between the modal displacements q_(si)(s) and the externalmicro force is given as $\begin{matrix}{{q_{si}(s)} = {\frac{{f_{c}(s)}\left( {{\Phi_{i}(L)} + {L_{0}\left\lbrack {{\Phi_{i}^{\prime}(L)} - {\Phi_{i}^{\prime}(0)}} \right\rbrack}} \right)}{\rho\quad{A\left( {s^{2} + \omega_{i}^{2}} \right)}}.}} & (25)\end{matrix}$

Based on equations (7) and (9), since ω_(s)(r,s)=Σ_(i=1)^(∞)Φ_(i)(r)q_(si)(s), by Laplace transform of equation (7), Q_(s)(s)can be represented as $\begin{matrix}\begin{matrix}{{Q_{s}(s)} = {{{- {cE}_{s}}d_{31}W\quad{\omega_{s}^{\prime}\left( {r,s} \right)}}|_{0}^{L}}} \\{= {{- {cE}_{s}}d_{31}W{\sum\limits_{i = 1}^{\infty}{\left\lbrack {{\Phi_{i}^{\prime}(L)} - {\Phi_{i}^{\prime}(0)}} \right\rbrack{q_{si}(s)}}}}}\end{matrix} & (26)\end{matrix}$Substituting equation (26) into equation (9), then we have$\begin{matrix}{{V_{s}(s)} = {C_{s}{\sum\limits_{i = 1}^{\infty}{\left\lbrack {{\Phi_{i}^{\prime}(L)} - {\Phi_{i}^{\prime}(0)}} \right\rbrack{{q_{si}(s)}.}}}}} & (27)\end{matrix}$where $C_{s} = \frac{{- {cE}_{s}}d_{31}{W.}}{C_{p}}$

Subsequently, by combining equations (25) and (27), we have the dynamicsensing model, which denotes the relationship between the output voltageV_(s) of PVDF sensing layer 24 and the external micro force f_(c) at thesensor tip as follows: $\begin{matrix}{\frac{V_{s}(s)}{f_{c}(s)} = {C_{s}{\sum\limits_{i = 1}^{\infty}{\left\{ {\frac{\left\lbrack {{\Phi_{i}^{\prime}(L)} - {\Phi_{i}^{\prime}(0)}} \right\rbrack{\Phi_{i}(L)}}{\rho\quad{A\left( {s^{2} + \omega_{i}^{2}} \right)}} + \frac{{L_{0}\left\lbrack {{\Phi_{i}^{\prime}(L)} - {\Phi_{i}^{\prime}(0)}} \right\rbrack}^{2}}{\rho\quad{A\left( {s^{2} + \omega_{i}^{2}} \right)}}} \right\}.}}}} & (28)\end{matrix}$

To achieve the sensing voltage V_(s), the PVDF sensing layer 24 iselectrically coupled to a sensing circuit. In an exemplary embodiment,the sensing layer 24 is interfaced with a PCI-DAS4020/12 analog/digitalinput/output board (Measurement Computing Co.) using the electronicbuffer circuit as illustrated in FIG. 2. The buffer circuit isconstructed using a chopper stabilized operational amplifier TC7650C(Microchip Co.) with a high input impedance 10¹²Ω and low bias current1.5 pa (or alternatively ultra low bias current operational amplifiersAD549 (Analog Devices Co.) and OPA111 (Texas Instruments). Thus, thecircuit is used to buffer the open circuit voltage V_(s) of the sensinglayer. Resistor R_(in)>10⁹Ω provides a DC current path. The circuitoutput V_(so) is a high pass filtered approximation of the voltage V_(s)and can be sampled by the board which is in turn passed on to a PC. Thetransfer function between V_(so) and V_(s) can be represented as:$\begin{matrix}{\frac{V_{so}(s)}{V_{s}(s)} = {\frac{{sR}_{in}C_{p}}{\underset{C_{b}}{\underset{︸}{1 + {{sR}_{in}C_{p}}}}}.}} & (29)\end{matrix}$To further remove the 60 Hz noise from the data acquisition system, azero phase notch filer is added in the data collection program.

To interface with the sensing circuit, an electrode layer covers thesurface of the sensing layer 24. Although the electrode layer may fullycover the sensing layer as shown in FIG. 3A, it is envisioned that theelectrode layer may be patterned onto the surface of the sensing layer.In general, patterned electrodes are achieved during PVDF filmmanufacturing by screen printing conductive inks, metal masking duringsputtered electrode deposition, or chemically etching patterns byphotolithographic techniques. Exemplary patterns for the electrode layerare shown in FIGS. 3B-3J. The reasons for using vary shaped electrodepatterns are: (1) re-configure the effective active sensing or actuatingarea corresponding to the stress concentrating area of the bendingcantilever beam; and (2) reduce the pyroelectric effect and thermaldrifts being directly proportional to the big active area, the addedelectrode patches can help to reject the thermal and common-mode noisesusing a differential measuring compensation principle; (3) enhance thegeneration of a tip out-of-plane force by the actuating layer as well asthe detection of the tip out-of-plane velocity by the sensing layer, sothat the distributed sensor/actuator pair could be used for feedbackcontrol with unconditional stability; (4) the reduced electrode layerbrings down the closed circuit possibility of the electrodes of bothsensing and actuating layers; (5) activate the measurement of torque anddetection of torsion deformation of sensor beam due to the appliedforce; (6) enable the multi-point self-sensing so as to obtain feedbacksof strain, bending angle, bending moment, shear force and load of thesensor beam for stability of active servo control. (7) the shapedelectrode layer can sense and control individual modes in the structure,this enables a feedback controller to be realized in terms of a suitablyshaped area. It should be noted that an electrode layer of the samedesign is also patterned onto the actuator layer symmetrically.

Finally, by considering the whole sensing system, the global transferfunction is $\begin{matrix}{\frac{V_{so}(s)}{f_{c}(s)} = {C_{b}C_{s}{\sum\limits_{i = 1}^{\infty}{\left\{ {\frac{\left\lbrack {{\Phi_{i}^{\prime}(L)} - {\Phi_{i}^{\prime}(0)}} \right\rbrack{\Phi_{i}(L)}}{\rho\quad{A\left( {s^{2} + \omega_{i}^{2}} \right)}} + \frac{{L_{0}\left\lbrack {{\Phi_{i}^{\prime}(L)} - {\Phi_{i}^{\prime}(0)}} \right\rbrack}^{2}}{\rho\quad{A\left( {s^{2} + \omega_{i}^{2}} \right)}}} \right\}.}}}} & (30)\end{matrix}$Based on this equation, we can obtain the micro force f_(c)(t) and forcerate f_(c)(t) by measuring the output voltage V_(so)(t) of the sensinglayer when the initial values f_(c)(t₀) and V_(so)(t₀) are known.

The actuator layer 22 serves as a distributed parameter actuator forbalancing the deflections of the external micro force. The use of thisactuator can virtually improve the stiffness of the high sensitiveactive sensor structure, so as to enhance the manipulability of flexiblesensor and increase the dynamic range when it is mounted at the free endof a micromanipulator.

If a voltage V_(a)(r,t) is applied to the actuating layer 22, it inducesa longitudinal stress σ_(a) on the layer given by: $\begin{matrix}{{\sigma_{a}\left( {r,t} \right)} = {\frac{E_{a}d_{31}}{H_{a}}{V_{a}\left( {r,t} \right)}}} & (31)\end{matrix}$where E_(a) is the Young's modulus of the actuating PVDF film and H_(a)is the thickness of the PVDF actuating layer 22. The stress due to anapplied voltage produces a bending moment M_(a) along the compositesensor beam's neutral axis given by [20]: $\begin{matrix}{M_{a} = {{\int_{\frac{H_{m}}{2}}^{\underset{\_}{H_{m} + H_{a}}}{{\sigma_{a}\left( {r,t} \right)}{Wy}\quad{\mathbb{d}y}}} = {C_{a}{V_{a}\left( {r,t} \right)}}}} & (32)\end{matrix}$where$C_{a} = {\frac{1}{2}E_{a}d_{31}{{W\left( {H_{a} + H_{m}} \right)}.}}$Obviously, C_(a) is a constant which depends on both the geometry andthe material properties of the composite sensing/actuating beam.

To seek the transfer function between the actuating V_(a) and theelastic deflection of the sensor beam at any point along the beam,similar to the sensing layer equations, let's consider the deflection ofthe sensor beam only caused by the actuating layer 22, then aBernoulli-Euler equation with an additional terms due to the actuatingvoltage can be described as follows. $\begin{matrix}{{{\frac{\partial^{2}}{\partial r^{2}}\left\lbrack {{{EI}\frac{\partial^{2}{\omega_{a}\left( {r,t} \right)}}{\partial r^{2}}} - {C_{a}{V_{a}\left( {r,t} \right)}}} \right\rbrack} + {\rho\quad A\frac{\partial^{2}{\omega_{a}\left( {r,t} \right)}}{\partial t^{2}}}} = 0} & (33)\end{matrix}$where E, I, L, ρ are the same definitions as equation (10) above. V_(a)represents voltage across the actuating layer 22. ω_(a)(r,t) is thedeflection of the sensor beam caused by the actuating voltage V_(a).

Then the boundary conditions for the actuating equation are:$\begin{matrix}{{\omega_{a}\left( {0,t} \right)} = 0} & (34) \\{{{EI}\frac{\partial{\omega_{a}\left( {0,t} \right)}}{\partial r}} = 0} & (35) \\{{{El}\frac{\partial{\omega_{a}^{2}\left( {L,t} \right)}}{\partial r^{2}}} = {C_{a}{V_{a}\left( {L,t} \right)}}} & (36) \\{{{EI}\frac{\partial{\omega_{a}^{3}\left( {L,t} \right)}}{\partial r^{3}}} = 0} & (37)\end{matrix}$

Similarly, to follow the steps of modeling of the dynamic sensingequations, and using modal analysis method, we have the similarLagrange's equation of motion by $\begin{matrix}{{{\frac{\mathbb{d}}{\mathbb{d}t}\frac{\partial\left( {E_{ak} - E_{ap}} \right)}{\partial{\overset{.}{q}}_{ai}}} - \frac{\partial\left( {E_{ak} - E_{ap}} \right)}{\partial q_{ai}}} = U_{i}} & (38)\end{matrix}$Here, E_(ak) is the kinetic energy, E_(ap) represents the potentialenergy and U_(i) is the generalized non-conservative forces related tothe actuating moment. They are $\begin{matrix}{E_{ak} = {\frac{1}{2}{\int_{0}^{L}{{{\overset{.}{\omega}}_{a}\left( {r,t} \right)}^{2}\rho\quad A\quad{\mathbb{d}r}}}}} & (39) \\{E_{ap} = {\frac{1}{2}{\int_{0}^{L}{{EI}\quad{\omega_{a}^{''}\left( {r,t} \right)}^{2}\quad{\mathbb{d}r}}}}} & (40) \\{U_{i} = {{C_{a}\left\lbrack {{\Phi_{i}^{\prime}(L)} - {\Phi_{i}^{\prime}(0)}} \right\rbrack}{V_{a}(t)}}} & (41)\end{matrix}$where Φ is the shape mode as defined in sensing section. Notice that thevoltage V_(a) is constant along the length on the beam but undergoes astep change at each of the boundaries of this length.

Using the Lagrange's equation of motion (38) and orthogonalityconditions (17) and (20), we have the differential equationcorresponding to each shape mode to beEIα _(i) ⁴ q _(ai)(t)+ρA{umlaut over (q)} _(ai)(t)=C_(a)[Φ′_(i)(L)−Φ′_(i)(0)]V _(a)(t)   (42)Then by the Laplace transformation of the above equation, the dynamicrelationship between the modal displacements q_(ai)(s) and the inputvoltage V_(a)(s) is given as $\begin{matrix}{{q_{ai}(s)} = \frac{C_{a}{{V_{a}(s)}\left\lbrack {{\Phi_{i}^{\prime}(L)} - {\Phi_{i}^{\prime}(0)}} \right\rbrack}}{\rho\quad A\quad\left( {s^{2} + \omega_{i}^{2}} \right)}} & (43)\end{matrix}$This equation describes the modal displacements of the flexible beam dueto a voltage applied to the actuating layer 22.

Thus, the sensing layer 24 can detect the deformation of the sensorbeam, the information then is fed back to the actuating layer 22, theactuator will balance the deformation due to the external forces andkeep the sensor beam at the equilibrium position (straight). Oncebalance, the external force can also be equally achieved from thebalanced voltage V_(a) of the actuating layer 22 based on the activeservo transfer function between V_(a) and the force f_(c). To realizethis active behavior, the transfer function from the voltage applied tothe actuator layer 22 to the voltage induced in the sensing layer 24 orthe external force detected by the sensing layer 24 should be foundfirst.

To balance the deflection ω_(s)(r,s) detected by the sensing layer, anopposite deflection ω_(a)(r,s)=ω_(s)(r,s) exerted by the actuating layeris necessary. Assumed the shape mode is the same, to balance thedeflection, an opposite q_(si)(s) should be exerted by the actuatinglayer. To achieve the relationship between the sensing voltage V_(s) andthe balance voltage V_(a), by substituting the oppositeq_(ai)(s)=−q_(si)(s) in equation (43) into (27), then we have$\begin{matrix}{{V_{s}(s)} = {{- C_{s}}{\sum\limits_{i = 1}^{\infty}{\frac{{C_{a}\left\lbrack {{\Phi_{i}^{\prime}(L)} - {\Phi_{i}^{\prime}(0)}} \right\rbrack}^{2}{V_{a}(s)}}{\rho\quad A\quad\left( {s^{2} + \omega_{i}^{2}} \right)}.}}}} & (44)\end{matrix}$Continually, the transfer function between the sensing voltage V_(s) andthe balanced voltage V_(a) can be found as $\begin{matrix}{\frac{V_{a}(s)}{V_{s}(s)} = {- {\sum\limits_{i = 1}^{\infty}{\frac{\rho\quad A\quad\left( {s^{2} + \omega_{i}^{2}} \right)}{C_{s}{C_{a}\left\lbrack {{\Phi_{i}^{\prime}(L)} - {\Phi_{i}^{\prime}(0)}} \right\rbrack}^{2}}.}}}} & (45)\end{matrix}$

Sequentially, from equation (28), the active servo transfer functionbetween the external force acting at the sensor tip and the balancedvoltage V_(a) in the actuating layer can be given by $\begin{matrix}{\frac{V_{a}(s)}{f_{c}(s)} = {- \frac{\sum\limits_{i = 1}^{\infty}\frac{C_{s}\begin{pmatrix}{{\left\lbrack {{\Phi_{i}^{\prime}(L)} - {\Phi_{i}^{\prime}(0)}} \right\rbrack\quad{\Phi_{i}(L)}} +} \\{L_{0}\left\lbrack {{\Phi_{i}^{\prime}(L)} - {\Phi_{i}^{\prime}(0)}} \right\rbrack}^{2}\end{pmatrix}}{\rho\quad A\quad\left( {s^{2} + \omega_{i}^{2}} \right)}}{\sum\limits_{i = 1}^{\infty}\frac{C_{s}{C_{a}\left\lbrack {{\Phi_{i}^{\prime}(L)} - {\Phi_{i}^{\prime}(0)}} \right\rbrack}^{2}}{\rho\quad A\quad\left( {s^{2} + \omega_{i}^{2}} \right)}}}} & (46)\end{matrix}$The above transfer function equations can be used to generate thebalance force and to calculate the micro force applied to the sensor tipduring active servo balance. The active servo balance methodologies canbe PI, PID, LQR (linear quadratic regulator) compensation, LQG (linearquadratic Gaussian), Luenberger observer based compensator, Kalman-Bucyfilter, spatial H₂ norm, spatial H_(∞) norm. For themulti-electrode-patch pattern, DSFB (direct strain feedback), SFB (shearforce feedback) or BMFB (bending moment feedback) can be employed torealize active servo balance as the strain, shear force, bending momentof the sensor beam can be achieved.

An exemplary micro robotic system employing an active micro-force sensorof the present invention is further described below. The micro roboticsystem is mainly comprised of a SIGNATONE Computer Aided Probe Stationand a Mitutoyo FS60 optical microscope system. The micro robot iscontrolled by a PC-based control system. The system is an open platformwhich can easily be integrated with the active micro-force sensor of thepresent invention. To improve the active servo speed, real-timeimplementation of the proposed control algorithm was performed using anx86 based PC running Linux operating system. The RTAI (Real-timeApplications Interface) patch was used to provide POSIX compliant,real-time functionality to the Linux operating system.

The sensing voltage V_(s) is the input to the PCI-DAS4020/12 acquisitionboard through a buffer interface circuit as shown in FIG. 2. Based onthe transfer function (45), the balance signal (in the range of ±10V) isoutput to the same PCI-DAS4020/12 acquisition board, furthermore, thesignal is linearly amplified to approach to V_(a) by a power amplifierbuilt by high voltage FET-input operational amplifier OPA445 for thePVDF actuating. The maximum sampling frequency of PCI-DAS4020/12 is 20MHz with 12-bit AD resolution. The loop time of the force sensing andcontrol system is about 60 μs. To reduce the vibrations from theenvironment, an active vibration isolated table was used during theexperiments.

FIG. 4 depicts a block diagram of the active sensing system. As shown,it is a typical single-input-single-output feedback control loop. Thefeedback signal is generated by the sensing layer due to the externalforce at the sensor tip. The signal is conditioned by a buffer interfaceand filtered in the collection program. The signal is then adjusted andamplified to apply to the actuating layer 22 based on the transferfunction (45).

In this exemplary system, the active force sensor has the followingdimensions and parameters: L=0.01864868 m; W=0.00979424 m; L₀=0.0255778m; C_(P)=0.88×10⁻⁹ F; d₃₁=23×10⁻¹² C/N; c=102.5×10⁻⁶ m;H_(a)=H_(s)=45×10⁻⁶ m; H_(m)=125×10⁻⁶ M; E_(a)=E_(s)=2×10⁹ N/m²;E_(m)=3.8×10⁹ N/m²; P_(a)=P_(s)=1.78×10³ Kg/m³; P_(m)=1.39×10³ Kg/m³. Itwill be appreciated that these types of the systems may be constructedwith many different configurations, components, and/or values asnecessary or desired for a particular application. The aboveconfigurations, components and values are presented only to describe oneparticular embodiment that has proven effective and should be viewed asillustrating, rather than limiting, the present invention.

The transfer function between the actuating voltage V_(a) and thesensing voltage V_(s) is a key for active sensing. Using the V_(a)/V_(s)transfer function, the frequency response of the active sensor isdemonstrated by simulation as shown in FIG. 5A. To test the model, weexert the known voltage signal in the range of ±30V to the actuatinglayer, then record the sensing voltage due to the deflection of sensorbeam. FIG. 5B shows the experimental result in the relationship betweenthe V_(a) and V_(s). It can be observed that the two Bode results(comparison of three shape modes) are very close and verify theeffectiveness of the developed transfer function model. For this activesensor, the frequency of the first shape mode is about 69 Hz, the secondshape mode is 1.2 KHz, the third one is about 2.9 KHz. In summary, tobalance the external micro force, by feedback the sensing voltage to theactuating layer through the transfer function (45) in real time, theactive micro-force sensor of the present invention can be realized.

In addition, the two composite active PVDF films with differentpyroelectric orientations can be chosen to construct a parallel-beamstructure, then two voltage variations ΔV_(pyro) due to pyroelectriceffect in two PVDF beams are opposed. As the two films are connected inparallel at the input of the buffer interface circuit or the amplifiercircuit, then the pyroelectric effects of this kind of structure can beself compensated. Based on the active parallel-beam structure with thefunction of self thermo-compensation, a multi-axis (3-D) active microforce sensor is also designed as shown in FIG. 6. The active beams ofthe sensor are aligned perpendicularly to each other, so the 3-D sensorstructure also provides a decoupled force measurement in threedirections. The sensing model of PVDF sensing layers in a parallel beamconstruction can be developed based on the formulations of the one-piececantilever construction described above.

The description of the invention is merely exemplary in nature and,thus, variations that do not depart from the gist of the invention areintended to be within the scope of the invention. Such variations arenot to be regarded as a departure from the spirit and scope of theinvention.

1. An active micro-force sensor for use on a micromanipulation device,comprising: a cantilever structure in a form of a plate which extendslengthwise away from a connection point to the micromanipulation device,the cantilever structure having an actuator layer of piezoelectricmaterial and a sensing layer of piezoelectric material; and a contacttip or tool extending outwardly from the cantilever structure at adistal end from the connection point to the micromanipulation device. 2.The active micro-force sensor of claim 1 further comprises a sensingcircuit electrically coupled to the sensing layer and operable tomeasure an output voltage thereon.
 3. The active micro-force sensor ofclaim 2 wherein the sensing circuit is further operable to determine arate of change of a force exerted on the contact tip or tool.
 4. Theactive micro-force sensor of claim 1 further comprises: a sensingcircuit electrically coupled to the sensing layer and operable todetermine a force exerted on the contact tip or the tool, where theforce causes a deformation of the cantilever structure; and an actuatingcircuit electrically coupled to the actuator layer and operable to applya voltage thereto which causes a deformation of the cantilever structurethat counteracts the deformation caused by the force exerted on thecontact tip or the tool.
 5. The active micro-force sensor of claim 4wherein the actuating circuit is adapted to receive a signal indicativeof the force exerted on the contact tip or the tool from the sensingcircuit and operable to apply the voltage to the other layer based onsaid signal.
 6. The active micro-force sensor of claim 5 wherein theactuating circuit is operable to determine a force exerted on thecontact tip or the tool from the voltage applied to the actuating layer.7. The active micro-force sensor of claim 1 wherein the cantileverstructure having a substantially rectangular shape.
 8. The activemicro-force sensor of claim 1 wherein the piezoelectric material isfurther defined as a polyvinylidene fluoride material or a leadzirconate titanate material.
 9. The active micro-force sensor of claim 1wherein the actuator layer and sensing layer are bonded directlytogether using an insulating, elastic adhesive.
 10. The activemicro-force sensor of claim 1 further comprises a support layerinterposed between the actuator layer and the sensing layer.
 11. Theactive micro-force sensor of claim 10 wherein the support layer iscomprised of a polyester material with a function of electrostaticshielding.
 12. The active micro-force sensor of claim 10 wherein thesensing layer and actuating layer are symmetrically patterened onto thesupport layer using either screen printing conductive inks, metalmasking during sputtered electrode deposition or chemically etchingpatterns by photolithographic techniques.
 13. An active micro-forcesensor for use on a micromanipulation device, comprising: a cantileverstructure in a form of a plate which extends lengthwise away from aconnection point to the micromanipulation device, the cantileverstructure having a support layer disposed between two outer layersconsisting of a piezoelectric material; and a contact tip or a toolextending outwardly from the cantilever structure at a distal end fromthe connection point to the micromanipulation device.
 14. The activemicro-force sensor of claim 13 further comprises a sensing circuitelectrically coupled to one of the two outer layers and operable tomeasure an output voltage thereon.
 15. The active micro-force sensor ofclaim 14 wherein the sensing circuit is further operable to determine arate of change of a force exerted on the contact tip.
 16. The activemicro-force sensor of claim 13 further comprises: a sensing circuitelectrically coupled to one of the two outer layers and operable todetermine a force exerted on the contact tip or the tool, where theforce causes a deformation of the cantilever structure; and an actuatingcircuit electrically coupled to the other of the two outer layers andoperable to apply a voltage thereto which induces a longitudinal stressthat counteracts the deformation caused by the force exerted on thecontact tip.
 17. The active micro-force sensor of claim 16 wherein theactuating circuit is adapted to receive a signal indicative of the forceexerted on the contact tip or the tool from the sensing circuit andoperable to apply the voltage to the other layer based on said signal.18. The active micro-force sensor of claim 13 wherein the cantileverstructure having a substantially rectangular shape.
 19. The activemicro-force sensor of claim 13 wherein the piezoelectric material isfurther defined as a polyvinylidene fluoride material or a leadzirconate titanate material.
 20. The active micro-force sensor of claim13 wherein the support layer is comprised of a polyester material. 21.An active micro-force sensor for use on a micromanipulation device,comprising: a cantilever having a first set of two substantiallyrectangular plates having longitudinal surfaces oriented parallel toeach other, where the first set of two rectangular plates extendslengthwise from a connection point on the micromanipulation device, anda second set of two substantially rectangular plates having longitudinalsurfaces oriented parallel to each other and coupled to the first set oftwo rectangular plates at a distal end from the connection point to themicromanipulator, wherein each plate in the first set and the second setof rectangular plates includes at least two layers of piezoelectricmaterial; and a connecting member extending between the two rectangularplates of the second set at an outermost lengthwise end and defining anoutwardly facing surface area, such that a contact tip or a tool extendsoutwardly from the outwardly facing surface area of the connectingmember.
 22. The active micro-force sensor of claim 21 wherein thelongitudinal surface of the second set of two rectangular plates extendslengthwise from the first set of two rectangular plates such that alength dimension of the two rectangular plates in the second set aresubstantially in parallel with a length dimension of the two rectangularplates in the first set and a width dimension of the two rectangularplates in the second set are substantially perpendicular to a widthdimension of the two rectangular plates in the first set.
 23. Amicroforce sensing system, comprising: a force sensor having a contacttip or a tool extending outwardly from a cantilever structure andoperable to detect a contact force exerted on the contact tip or thetool, wherein the cantilever structure includes an actuator layer ofpiezoelectric material and a sensing layer of piezoelectric material;and a processing circuit adapted to receive a sensing signal indicativeof the contact force from the sensing layer and operable to feed abalance signal to the actuator layer.
 24. A micro robotic system,comprising: a micromanipulator; an active force sensor having acantilever structure in a form of a plate which extends lengthwise froma connection point to the micromanipulator and a contact tip or a toolextending outwardly from the cantilever structure at a distal end fromthe connection point the micromanipulator, wherein the cantileverstructure includes an actuator layer of piezoelectric material and asensing layer of piezoelectric material bonded together; and a positiondetector adapted to capture displacement data for the contact tip or thetool of the active force sensor during a manipulation operation.